Soil erosion and sediment transport play important roles in terrestrial
landscape evolution and biogeochemical cycles of nutrients and contaminants.
Although discharge is considered to be a controlling factor in sediment
transport, its correlation with sediment concentration varies across the
Yellow River basin (YRB) and is not fully understood. This paper provides
analysis from gauges across the YRB covering a range of climates, topographic
characteristics, and degrees of human intervention. Our results show that
discharge control on sediment transport is dampened at gauges with large mean
annual discharge, where sediment concentration becomes more and more stable.
This emergent stationarity can be attributed to vegetation resistance. Our
analysis shows that sediment concentration follows a bell shape with
vegetation index (normalized difference vegetation index, NDVI) at an annual
scale despite heterogeneity in climate and landscape. We obtain the
counterintuitive result that, as mean annual discharge increases, the dominant
control on sediment transport shifts from streamflow erosion to vegetation
retardation in the YRB.

Watershed sediment transport, from hillslope to channel and subsequently the
coast, is crucial to erosion management; flood control; river delta
development; and the quantification of global biogeochemical cycles of
materials such as organic phosphorus, iron, and aluminum (Martin and
Meybeck, 1979; He et al., 2014). During the 20th century, human
activities significantly modified the landscape, leading to a reduction
in sediment yield and coastal retreat worldwide (Walling and Fang, 2003;
Syvitski et al., 2005). Known for its severe sediment problems, the Yellow
River (YR) has been a hotspot for studies on soil erosion and sediment
transport for decades. Since the 1950s, the annual sediment yield has
declined by 80 % because of check-dam construction and ecosystem
restoration such as the Grain-for-Green project, motivating discussion on
the necessity for further expansion of revegetation schemes (Chen et al.,
2015).

Most studies on the physical mechanisms of soil erosion and sediment
transport were conducted in relatively small sub-catchments (Collins
et al., 2004; Ran et al., 2012). In order to interpret the patterns
discovered at the basin scale, it is essential to understand the scaling
effects of soil erosion and sediment transport. Specifically, would the
mechanisms identified at a small scale also prevail at the basin scale? If not,
what factors influence upscaling (Mutema et al., 2015; Song et al.,
2016)? However, existing studies on the scaling effects of sediment
transport are rather limited and show no significant spatial coherence in
the scaling of sediment transport (Le Bissonnais et al., 1998; Deasy
et al., 2011; Song et al., 2016). Due to the great heterogeneity in the YRB,
scaling patterns could be different even within one tributary. Taking the
Wuding River as an example, event mean concentration could decrease downstream
after the initial increase in one sub-catchment (Zheng et al., 2011)
or keep rising until reaching a plateau in another sub-catchment nearby
(Fang et al., 2008). Not only the sediment concentration, but also its
correlation with discharge varies across the YRB. Although discharge is
considered to be one of the controlling factors in sediment transport, how its
influence upscales remains to be fully understood. Therefore it is necessary
to expand our findings concerning sediment transport from single tributaries
to larger scales, especially incorporating diverse climate, environmental,
and anthropogenic characteristics, so that we can derive an understanding
applicable to the whole YRB. In this paper, we collected observations across
the Yellow River basin (YRB) to quantify changes in sediment concentration
in the recent decades (Rustomji et al., 2008; Miao et al., 2011; Wang
et al., 2016). By analyzing data from gauges across the YRB (Fig. S1 in the Supplement), we
attempt to understand how the correlation between sediment concentration
and discharge varies across spatial and temporal scales, what are the
dominant factors influencing sediment transport in the YRB, and how their
contributions vary from place to place.

We collected daily discharge and sediment concentration data from 123
hydrology gauges within our study area: the YRB above the Sanmenxia station, which is the
major hydropower station on the YR. From these we selected 68 gauges
spanning a range of climate conditions and physiographic areas, from the
gauge at the most upstream end of the main stem to the gauges above
Tongguan, which is just 100 km upstream of Sanmenxia Dam (Fig. S1). These
gauges were selected for at least 15-year (1971–1986) continuous daily
discharge and sediment concentration records between 1951 and 1986. For
comparison and further examination of our hypothesis, we also extract the
annual discharge and concentration data between 2000 and 2012 for seven
gauges located at the outlet of the major tributaries from the Yellow River Sediment Bulletin (Fig. S1 green stars).

The vegetation data used in this study correspond to the normalized
difference vegetation index (NDVI), which is an index calculated from remote
sensing measurements to indicate the density of plant growth (Running et
al., 2004). The NDVI data were downloaded from NASA's Land Long Term Data
Record (LTDR) project, which provides daily NDVI observations globally at a
spatial resolution of 0.05∘. Instead of the NDVI obtained from Global
Inventory Modeling and Mapping Studies (GIMMS), the NDVI from the LTDR project
is chosen for its better estimation in the YRB (Sun et al., 2015).
The daily NDVI data from 44 gauges located on the eight major tributaries
were collected and extracted according to the drainage area of the study
gauges from 1982 to 2012 (Fig. S1 green stars). The gauges on the main
stem of the YR were not used as the water and sediment condition there is more
likely controlled by the major dams along the main stem rather than the
hillslope characteristics. Annual maximum NDVI values were used to represent
the highest vegetation productivity. The precipitation and leaf area index
(LAI) data of the US catchments used for comparison are assembled from the
first author's previous work (Ye et al., 2015).

To examine the coupling between discharge and sediment concentration at
various temporal scales, wavelet coherence analysis was applied to the daily
discharge (m3 s−1)
and sediment concentration (kg m−3) data following
Grinsted et al. (2004). Wavelet transforms decompose time series into
time and frequency and can be used to analyze different parts of the time
series by varying the window size. They have been applied to geophysical
records for the understanding of variability at temporal scales. To examine
the co-variation between discharge and concentration in the time frequency
domain, we used a wavelet coherence defined as (Grinsted et al., 2004)

(1)R2s=|Ss-1WXYs|2Ss-1WXs2⋅S(s-1|WYs|2),

where S is a smoothing operator, WXY is the cross-wavelet transform of time
series X and Y representing the common power between the two series, s refers
to the scale, and WX and WY are the continuous wavelet transforms of time
series X and Y respectively. The wavelet coherence can be considered a
correlation coefficient of the two time series in the time frequency domain.
The region of cone of influence (COI) was delineated in the wavelet
coherence images to avoid reduction in confidence caused by edge effects.
Localized wavelets were also averaged through temporal scales to obtain
global wavelet coherence (Guan et al., 2011). More detailed
explanation about wavelet coherence analysis can be found in Grinsted et
al. (2004).

The annual discharge (Qa) and the sediment yield (La) were
aggregated daily to further examine their correlation:

(2)Qa=∑i=1n(Qi⋅3600⋅24)/Ad⋅1000,(3)La=∑i=1n(Qi⋅Ci⋅3600⋅24),

where Qi (m3 s−1) and Ci (kg m3) are the daily discharge
and sediment concentration, Ad is the drainage area (km2) of each gauge,
and n is the number of days in each year. This analysis is applied only at an annual
scale since this is when the coupling from wavelet coherence analysis is the
strongest (the one with the largest wavelet coherence). The annual mean
concentration (Ca) was calculated as

(4)Ca=La/(Qa⋅Ad/1000).

The long-term mean annual discharge (Qm) and the long-term mean annual
concentration (Cm) were also calculated by averaging for the period of
1951 to 1986. Note that both the parameters Qa and Qm used here are
area-specific discharges (mm yr−1). For each gauge, a linear regression was
fit to describe the correlation between annual discharge (Qa) and annual
mean concentration (Ca). The slope of this linear regression (αQC) is used to describe the rate of change in sediment concentration
with changing discharge at an annual scale.

We applied wavelet coherence analysis to daily discharge and sediment
concentration data at 68 study gauges across the YRB (Figs. S2, S3). The
results show that, across the gauges, the coupling between discharge and
concentration (Q–C) declines with mean annual discharge (Qm) at all
three temporal scales (Fig. 1a). That is, as Qm increases, the
influence of streamflow on sediment transport becomes weaker and weaker
across the gauges, both at intra-annual and within-year scales.

This fading impact of streamflow as it increases can be further quantified
in terms of a linear regression between discharge (Qa) and mean sediment
concentration (Ca) at an annual scale, when the coupling between discharge
and concentration (Q–C) is the strongest (Fig. S4). As can be seen from
Fig. 1b, though annual mean concentration is positively correlated with
annual discharge at most gauges, the slope in the Q–C regression (αQC) declines exponentially with Qm across the gauges (p value
<0.0001). The larger Qm is, the less sensitive sediment
concentration responds to variation in annual discharge. For example, gauges
with αQC less than 0.1 are the ones with Qm larger than
60 mm yr−1. When Qm is larger than 100 mm yr−1, the variation in sediment
concentration is less than 1 % of that in streamflow (αQC<0.01),
and thus sediment concentration can be approximated as
invariant to changing discharge. Most of these gauges are located on the main
stem or near the outlets of tributaries. This increased independence between
sediment concentration and discharge may be attributed to the heterogeneity
in these relatively large catchments.

This emergent stationarity explains the linear correlation between
area-specific sediment yield and runoff depth reported in a small
sub-watershed in a hilly area of the Loess Plateau (Zheng et al.,
2013). Considering the sediment concentration to be constant, the variation
in yield is solely dominated by streamflow, resulting in the observed linear
discharge–yield relationship.
Similar stationarity in sediment concentration
has also been found in arid watersheds in Arizona, US (Gao et al., 2013),
where the sediment concentration becomes homogeneous among watersheds
when their drainage area is larger than 0.01 km2. The difference in
threshold for the emergence of approximately discharge-invariant
concentration between the YRB and watersheds in Arizona, US, is probably due
to the differences in catchment characteristics, i.e., vegetation type and
coverage, terrestrial structure, soil properties, etc.

Our analysis shows that mean annual discharge (Qm) is a better indicator
of the correlation between water and sediment transport than drainage area,
although the last parameter has been used traditionally. Despite the
heterogeneity, both the coupling between Q–C and the concentration
sensitivity to variation in streamflow decreases with Qm. A closer
inspection reveals useful insights. At gauges with smaller values of
Qm, discharge is the dominant factor in sediment transport: an increment
in annual discharge is amplified in the increment of sediment concentration
(αQC>1) (i.e., Gauge 808, 812 in Fig. S4).
However, as Qm increases, variation in streamflow is more weakly
reflected in variation in sediment concentration, even though annual mean
concentration still correlates with annual discharge, (i.e., Gauge 806 in
Fig. S4). As Qm continues to increase, sediment concentration becomes
almost invariant to discharge, suggesting that the dominant factor of
sediment transport has shifted from the discharge to something else.

To further explore the potential cause of this emergent stationarity, we
analyzed the vegetation data (NDVI) from 44 of the gauges located on eight
major tributaries of the YR (Fig. S1). Our analysis shows that this
declining sensitivity in concentration at an annual scale (αQC) is
negatively related to vegetation impact across the gauges (Fig. 2).

Figure 2Scatter plots between the maximum NDVI and slope in the
Q–C regression at an annual scale (αQC) from the 44 study gauges.

For gauges with limited vegetation establishment in their drainage area, the
variation in discharge is amplified in sediment transport (αQC>1). The larger the discharge is in a specific year, the
more sediment is eroded and mobilized per cubic meter. This dominance of
discharge is weakened when vegetation density and coverage increase. Despite
the larger sediment carrying capacity of larger discharge, sediment
concentration is reduced, probably due to the protection vegetation offers
against erosion. As maximum NDVI increases, sediment concentration becomes
less and less coupled with discharge at an annual scale. When the vegetation
density is sufficiently high, sediment concentration is nearly stable in
spite of the variation in discharge, since the dense vegetation coverage
protects soil from erosion and traps sediment. That is, the emergent
stationarity in sediment concentration corresponding to the variation in
discharge at gauges with large Qm can be attributed to the dampened
dominance of discharge due to the increasing impact of vegetation
retardation.

Figure 3Scatter plot of annual mean concentration and maximum
NDVI: (a) at 44 study gauges between 1982 and 1986, where the dots are
color-coded by the slope in the Q–C regression (αQC) at each
gauge; and (b) at seven gauges with both data from the years 1982 to 1986 (blue
dots) and the years 2008 to 2012 (red dots). The R2 for the two fits is
0.6 and 0.44 respectively with a p value <0.001 for both of them.

To further confirm the vegetation impact on sediment transport, we derived
the plot between maximum NDVI and mean concentration at an annual scale in
Fig. 3a. As we can see, the annual mean sediment concentration follows a
bell-shaped correlation with vegetation establishment, with a peak
concentration at a value of maximum NDVI of around 0.36. On the falling limb
of this bell curve, as NDVI increases, both sediment concentration and
αQC decrease consistently. That is, both the value of
concentration and its sensitivity to streamflow variation decline with
increasing vegetation index on the falling limb. To confirm this impact of
vegetation resistance, we also examined the relationship between sediment
concentration and other catchment characteristic like dominant soil type. No
significant correlation was observed.
Although there could
still be other factors not considered here that contributed to the decline in
sediment concentration, it is undoubted that vegetation is one of the most
influential factors of sediment reduction and can be used as a good
indicator of the soil erosion and sediment transport in the YRB.

On the rising limb, however, both the value of concentration and its
sensitivity to streamflow variation increase with increasing vegetation
index. Most gauges have values αQC larger than 1, except one
gauge with an extremely small maximum value of NDVI. For these gauges, on
the rising limb, vegetal cover is still low in an absolute sense despite
increasing NDVI. Sediment concentration is mainly dominated by discharge:
fluctuations in streamflow are amplified in concentration (αQC>1). The only gauge with a value of αQC
smaller than 1 is gauge Hanjiamao (HJM) at the Wuding River. Although the
annual precipitation and discharge at HJM is similar to other gauges along
the Wuding River, the annual mean sediment concentration is much smaller.
This is because of the extremely high baseflow contribution in discharge at
HJM, which is around 90 %, thanks to very intensive check-dam construction
there (Dong and Chang, 2014). Since sediment in the YRB is mostly
transported during large flow events during the summer, smaller flow events
are not capable of transporting significant sediment loads at HJM.

Figure 4Illustration of the correlation between vegetation and sediment
erosion, retardation, and the resulting sediment concentration in the YRB.
Since vegetation usually increases with discharge, with the rise in
discharge, sediment eroded and delivered by streamflow increases rapidly,
while the retardation from vegetation is limited at the beginning and
increases fast afterwards. This non-synchronous impact on sediment transport
leads to the bell shape correlation between sediment concentration and
vegetation.

In general, we can conclude that sediment transport is mainly dominated by
discharge when the vegetation index is low. With increasing NDVI, the impact
of vegetation grows slowly at first and accelerates after the maximum NDVI
exceeds 0.36. Eventually, the effect of NDVI takes over the dominance of
streamflow and attenuates the variation in sediment concentration (Fig. 4).
The nonlinear impact of vegetation in regard to resistance of sediment
to erosion is consistent with previous findings (Rogers and Schumm, 1991;
Collins et al., 2004; Temmerman et al., 2005; Corenblit et al., 2009). When
the vegetation index level is low, its resistance to soil erosion develops
slowly as vegetation grows and expands (Rogers and Schumm, 1991), and
the capability of vegetation to trap sediment is reduced when submerged by
flood (Temmerman et al., 2005) or overland flow. Therefore, for
catchments with limited vegetation establishment, the coverage of vegetation
is not sufficient to trap sediment, nor is the vegetation able to protrude
from the water level during the extreme flow events that transport most of
the sediment. Sediment transport in these catchments is usually dominated by
discharge. As NDVI increases, vegetation becomes much more capable as an
agent of erosion protection and sediment settling (Jordanova and
James, 2003; Corenblit et al., 2009). With the compensation from vegetation
retardation, sediment and discharge become more and more decoupled as
discharge increases, so concentration is nearly invariant to increasing
discharge. The transition point in maximum NDVI (around 0.36) is where the
increment in vegetation reduction balances with the incremental increase in
water erosion. When the capability of vegetation retardation catches up with
streamflow erosion, the net soil loss becomes negligible, a condition
commonly observed in well-vegetated regions.

In 1999, a large-scale ecosystem restoration project, the
Grain-for-Green project, was launched in the YRB for soil conservation (Lv
et al., 2012). It has substantially improved vegetation coverage after a
decade of implementation (Sun et al., 2015). To validate our
hypothesis gain from the early 1980s, we applied a similar analysis to the
annual flow and sediment data as well as daily NDVI data at seven gauges
located at the outlets of major tributaries from 2008 to 2012 (Fig. S1
green stars). This is the period subsequent to the initiation of the
Grain-for-Green project. We have excluded the years right after the
implementation of the Grain-for-Green project, when there was an initial
drastic change in vegetation coverage and sediment erosion and transport
processes.

As we can see from Fig. 3b, there is a significant increase in maximum NDVI
for all seven catchments and considerable reduction in mean sediment
concentration. This improvement is consistent with the previous report that
the Grain-for-Green project has made a remarkable achievement in regard to
soil conservation in the YRB (Chen et al., 2015). Comparison of the
relationship between sediment concentration and maximum NDVI in the early
1980s and around 2010 shows that the bell shape relationship is sustained even
after drastic and significant anthropogenic alteration of the land use and
land cover across the whole YRB. Although the vegetation coverage has
improved significantly at all seven comparison gauges due to the ecosystem
restoration policy, and therefore effectively moderated sediment erosion, the
bell shape relationship between maximum NDVI and mean concentration
is sustained.

Similar bell shape relationship was also found for the multi-year mean
annual precipitation and sediment yield observed in the United States (Langbein and Schumm, 1958).
The data used in the analysis of Langbein and
Schumm (1958) were collected in the 1950s from more humid and vegetated
catchments with limited human intervention, opposite to the YRB where the climate is arid and semi-arid,
vegetation coverage is low, and human activities are intensive.
However, a similar bell shape was still observed between sediment yield and
precipitation. Given the limited anthropogenic activities in these
catchments, vegetation growth is probably correlated with annual
precipitation due to its adaption to climate, as in other US catchments
(Fig. S6). Thus it is likely that a bell shape correlation between
vegetation and sediment yield would be found at these US catchments as well.
This suggests that the bell shape correlation between vegetation and
sediment concentration is not only observed in the YRB with intensive human
intervention, but could also be valid outside it. More analyses are needed
to test this relationship in other catchments outside the YRB for its
universality.

Our analysis shows that across the YRB both the correlation between Q and
C and the magnitude of sediment response to the variation in streamflow
decrease with Qm. When Qm is sufficiently large (i.e.,
>60mm yr−1), sediment concentration reaches a stationary (constant) state at
an annual scale. The emergent stationarity at gauges with large Qm is
related to the shift of dominance from discharge to vegetation. Because of
the slow development of vegetation resistance with increasing discharge for
small discharges, discharge dominates the soil erosion and sediment
transport process until the maximum NDVI exceeds a threshold (0.36 for this
study) at which the parameter governing concentration transits from
streamflow erosion to vegetation retardation.

Our findings of the emergent stationarity in sediment concentration and the
shift of the dominant mechanism governing the Q–C relation have important
implications for water and sediment management at the watershed scale. Our study
indicates that, for the gauges with relatively large discharge, the annual
mean concentration can be approximated as a constant over a large range of
discharges. Thus the estimation of sediment yield can be simply inferred
from a simulation of streamflow. First-order estimates of sediment yield for
scientific or engineering purposes can be obtained by multiplying the
estimated discharge by a constant sediment concentration estimated based
upon the vegetation index. The correlation between vegetation and sediment
concentration will also be useful for the design of the ongoing ecosystem
restoration program known as the Grain-for-Green project. The bell-shaped
correlation between maximum NDVI and sediment concentration provides a
quantitative way to estimate the potential change in sediment concentration
associated with proposed ecosystem restoration planning schemes at and near
each tributary. This can help guide land use management so as to allocate
the sediment contribution from each of the upstream tributaries in a way
that maintains the balance between erosion and deposition in the lower YR.

It is important to collect more data from the current decade (i.e., after the
substantial ecosystem restoration) to further validate our findings in
regard to emergent stationarity and vegetation impact at more gauges in the
YRB. It will be helpful if we could examine our findings in other watersheds
worldwide with different climate and vegetation types. Although humid
regions are usually considered to be well vegetated, studies show
that there could still be erosion issues in these areas due to topographic gradient,
precipitation intensity, and soil properties. (Holz et al., 2015).
Analysis with more field measurements could also help explain the threshold
discharge of the emergent stationarity. Numerical simulations as well as
long-term measurements on the soil properties are also needed to further
explain the physical mechanism of vegetation retardation: how it develops
its impact on soil erosion and sediment transport by changing soil
properties and other topographic characteristics during its growth and
spread.

This research was financially supported by the National Key Research and
Development Program of China (2016YFC0402404, 2016YFC0402406) and the
National Natural Science Foundation of China (51509218, 51379184, 51679209).
The authors thank Jinren Ni for insightful discussions.

Our study shows that there is declining coupling between sediment concentration and discharge from daily to annual scales for gauges across the Yellow River basin (YRB). Not only the coupling, but also the magnitude of sediment response to discharge variation decreases with long-term mean discharge. This emergent stationarity can be related to sediment retardation by vegetation, suggesting the shift of dominance from water to vegetation as mean annual discharge increases.

Our study shows that there is declining coupling between sediment concentration and discharge...